Ariel Rubinstein is a famous game theorist who has been arguing for a while that game theory is not useful. Most recently he published an op-ed in the Israeli Ha’aretz newspaper, mischievously entitled “How game theory will solve the Euro zone problems and stop the Iranian nukes?” (answer: it won’t). The op-ed rehashes his well-known views, but there was one paragraph that I particularly liked. (I’m translating from Hebrew because the English version of the op-ed, which appeared a few days ago under a slightly different title, is behind an insurmountable paywall.)
Some of the claimed applications of game theory are nothing but labels for real-life situations. For example, it has been claimed that the Euro zone crisis is like the games known as the prisoner’s dilemma, chicken, and the diner’s dilemma. The crisis bears a resemblance to all of these situations. But such statements are as hollow as saying that the Euro zone crisis is like a Greek tragedy. While the comparison to a Greek tragedy is perceived as an emotional statement by ivory tower intellectuals, giving a label from the game theory lexicon is for some reason perceived as a scientific truth.
A few days later the New York Times published an article that seems to have been deliberately designed to piss Rubinstein off. Michael Chwe, a UCLA political science professor, has just published a book called “Jane Austen, Game Theorist”. I haven’t read the book itself, but what I can say is that the NYT story makes a weak case for why Jane Austen “isn’t merely fodder for game-theoretical analysis, but an unacknowledged founder of the discipline itself”. For example:
Take the scene in “Pride and Prejudice” where Lady Catherine de Bourgh demands that Elizabeth Bennet promise not to marry Mr. Darcy. Elizabeth refuses to promise, and Lady Catherine repeats this to Mr. Darcy as an example of her insolence — not realizing that she is helping Elizabeth indirectly signal to Mr. Darcy that she is still interested. It’s a classic case of cluelessness, which is distinct from garden-variety stupidity, Mr. Chwe argues. “Lady Catherine doesn’t even think that Elizabeth” — her social inferior — “could be manipulating her,” he said.
But if, as Rubinstein “suggests”, Greek tragedies capture strategic interactions, and if we’re anyway revising our view of who founded game theory, shouldn’t the honor go to Sophocles?
Turing's Invisible Hand 
Another relevant book which discusses game theory in literature (as well theology, philosophy, and history) is the one by Brams (http://www.amazon.com/Game-Theory-Humanities-Bridging-Worlds/dp/0262015226).
As Norman Geras writes here (http://normblog.typepad.com/normblog/2013/04/game-theorist-jane.html):
“Is Chwe really on to anything other than what large numbers of Austen’s readers could have told you yesterday or even last week: that she had a sharp intelligence and an astute grasp of the intricacies of human motive and interaction?”
The English version is (so far freely) accessible from the German newspaper Frankfurter Allgemeine Zeitung at
http://www.faz.net/aktuell/feuilleton/debatten/game-theory-how-game-theory-will-solve-the-problems-of-the-euro-bloc-and-stop-iranian-nukes-12130407.html
Thanks! It’s amusing to compare the two translations of the same paragraph:
“Some of the arguments for using game theory do nothing more than attach labels to real-life situations. For example, some contend that the Euro Bloc crisis is like the games called Prisoner’s Dilemma, Chicken or Diner’s Dilemma. The crisis indeed includes characteristics that are reminiscent of each of these situations. But such statements include nothing more profound than saying that the euro crisis is like a Greek tragedy. While the comparison to a Greek tragedy is seen as an emotional statement by detached intellectuals, the assignment of a label from the vocabulary of game theory is, for some reason, accepted as a scientific truth.”
Rubenstein is right. Much of what passes for analysis is labelling, and not good taxonomy either.
But, game theory can provide an important role in identifying strategic situations as similar because formally equivalent.
Chwe does a nice introductory job with this in his 2005 article Rational Choice and the Humanities: Excerpts and Folktales showing the strategic similarity between Much Ado About Nothing and Richard Wright’s Black Boy.
Whether his demonstration of formal equivalence lead to further strategic insights, which could have not been had but for use of game theory, is something that needs further work.
Thanks all! I think that there are some real insights in the book, so please check it out. At a conference in Stockholm, Rubinstein saw me present some of the material in the book, and I didn’t detect any scowls or frowns, so I think he is OK with it! [smile] Both Rubinstein and I are pushing the idea of models as being like fables or folktales, simplified descriptions of a situation (which everyone knows is simplified and unreal) which still provide an insight which you can bring back to the real world.
As for Austen, the book argues that Austen was not just a keen observer of human behavior. The book argues (at great, perhaps too great, length!) that Austen develops a nascent theory of utility (for example, she includes many examples of how you might think different kinds of pleasures and pains are incommensurable but in fact they are commensurable), purposefully set up examples to compare different kinds of explanations for a phenomenon (i.e. discussing whether a behavior is due to rational choice or due to habit), considers game-theoretic questions like how it can be welfare-improving to _not_ have to make a choice, analyzes how people learn to think strategically, and so forth.
Austen’s largest contribution is her analysis of why high-status people have difficulty seeing low-status people as strategic, and how low-status people take advantage of this.
Thanks! Michael
Thanks for the nice comment Michael. I was trying to avoid saying anything about the book itself because I haven’t read it or even seen it (I would have been even more explicit about this if I knew you would read the post!). As for Rubinstein’s views, my interpretation is that he would have pushed back against statements like “her [Austen’s] observations apply to US military blunders in Iraq and Afghanistan” (from http://www.sscnet.ucla.edu/polisci/faculty/chwe/austen/), which I take to mean that game theory applies to these situations, but I don’t know him and in fact I don’t agree with his view that game theory is not useful (https://agtb.wordpress.com/2012/06/17/is-game-theory-useful/).
Michael writes:
“Both Rubinstein and I are pushing the idea of models as being like fables or folktales, simplified descriptions of a situation (which everyone knows is simplified and unreal) which still provide an insight which you can bring back to the real world.”
I don’t think this right.
The game theoretic model must capture something insightful about the real world first.
Then you find an other instance of the model -where it might be hard to see the original insight because the similarities of the situations were not obvious.
Hi Ariel and Michael—my take on Rubinstein’s articles is that he is arguing that one shouldn’t try to claim expertise just because one has a game theory model, which I think is a good point. I myself think game theory is very useful.
On how to properly build models, I can only speak for myself. I usually start by doing the modeling and then try to apply it to reality and hope it works. In other words, I personally don’t start with reality. For example, in my 2001 book “Rational Ritual,” I started with the concept of common knowledge (often considered a highly abstract topic, especially back then) and then tried to find examples in real life. I ended up arguing that rituals, watching the Super Bowl, etc., are examples of common knowledge generation. I did not start by looking at actual real-world rituals.
There are famous cases in which people start with reality and then end up with something quite abstract (Satterthwaite’s theorem is an example), so both directions are possible.
Thanks! Michael
I find the comparison to Greek tragedies relieving 🙂 And it complements well Aumann’s essay “What is game theory trying to accomplish” (e.g. this fragment:
“An alternative way of viewing game theory and mathematical economics is as art forms. […] In game theory and mathematical economics, the resistive medium is the mathematical model, with its definitions, axioms, theorems and proofs. Because we must define our terms, state our axioms and prove our theorems precisely, we are forced into a discipline of thought that is absent from, say, verbal economics.
If one thinks of mathematics as art, then one can think of pure mathematics as abstract art, like a Bach fugue or a Pollock canvas (though often even these express an emotion of some kind); whereas game theory and mathematical economics would be expressive art, like a cubist painting or Tolstoy’s War and Peace. We strive to make statements that, while perhaps not falsifiable, do have some universality, do express some insight of a general nature; we discipline our minds through the medium of the mathematical model; and at their best, our disciplines do have beauty, simplicity, force and relevance.”)
@Michael and Ariel about the usefulness of Game Theory.
(I am reading Michael’s book and the paper Ariel had referenced regarding security games, and will have a longer note on both.)
On the usefulness of Game Theory, we have to ask (3) questions.
1. Useful to who and for what purpose?
2. What is the evidence that it was useful to the group’s purpose identified in 1?
3. Finally, was game theory indispensable or could the result/job identified in 1 been done better with some other tool.
For example, it is relevant to ask whether Michael’s game theoretic analysis of Much Ado about Nothing shed light on some Shakespearean controversy. It would be relevant to ask whether Ariel’s paper changed Airport security.
Without these sorts of questions, game theory is always useful: to those people who write about game theory for prestige and advancement in the academic community.
Thanks for reading my book, by the way! Michael
It is nice to return to the topic of “how useful is game theory?” Certainly the issue of how (when and if) game theory is useful is a central issue for game theorists. It is natural (and even instructive) that common tendency among specialist is perhaps overly positive, and it is natural that the issue is controversial.
I think we should compare game theory to two related mathematical areas. Statistics and optimization. (In fact, game theory is sometimes regarded as an extension of optimization from one agent to a number of strategic agents.)
For example, statistical studies led to the clear understanding that smoking causes cancer. Is there a clear-cut example of a similar nature for Game theory?
It is probably agreed that implications of game theory are rather limited and that usually game theory does not give definite or surprising answers of the level we see for smoking/cancer. I do not agree that modeling strategic behavior, which is what game theory is about, have no value in understanding real-life situations or in designing real-life mechanisms.
I like your implicit rephrasing of the question: Instead of “is game theory useful?”, you’re asking “how useful is game theory?”.
Hi all—I don’t think you can prove anything with game theory (unlike statistics). Most social scientists are a little wary of trying to “prove” anything!
Here is a specific example of how I think game theory is useful, from my book “Rational Ritual.” Why are Super Bowl commercials so expensive? It costs an advertiser around $4m for a Super Bowl slot.
The most obvious answer is that many people watch the Super Bowl. But this is not a complete answer, because the Super Bowl is very expensive even per viewer. This is true for popular TV shows in general (the data is described in my book). In other words, an advertiser could take the $4m it spends on the Super Bowl and spend it on other less popular TV shows and get roughly twice as many exposures.
The next common answer is that Super Bowl commercials demand one’s attention, people watch them again on Youtube, and they get press coverage. So the Super Bowl commercial gets exposed to more people than just those who watch the commercials “directly” during the game. This answer makes sense, but it does not explain another aspect of Super Bowl advertising: the kinds of goods advertised on the Super Bowl.
What you do see are beer and soft drinks, movies, cars, financial services (like Visa and Discover), communications (FedEx), and websites like monster.com. These goods roughly speaking are goods which a person is more likely to buy if she thinks others will buy them too (buying them is a “coordination problem”). Goods like Duracell batteries, breakfast cereal, and motor oil are not advertised on the Super Bowl—when I buy Duracell batteries, I do not care if others buy them too.
If Super Bowl commercials are expensive because they generate press coverage and make each individual pay more attention, it seems like this would apply to cars and Duracell batteries equally, so this cannot be the complete explanation.
The explanation offered by game theory (in my book Rational Ritual) is that if I am more likely to watch Iron Man 3 or put my resume on monster.com if I know others will do the same, then when I see the ad on the Super Bowl, not only do I see the ad, I know that others see the same ad. In other words, the Super Bowl generates not only knowledge of the product but also “metaknowledge” of the product. Advertisers of “coordination problem” goods are willing to pay extra for this metaknowledge, because if they advertised on many unpopular shows, no viewer would infer from watching a commercial that anyone else is watching it too.
This explanation could be right or wrong (I think the data back it up) but it is a new kind of explanation which did not exist before game theory. At the very least, this explanation suggests that the model of advertising which thinks about a message being sent from an advertiser to an individual (i.e. an explanation based on the Super Bowl’s salience to individual viewers) is incomplete, and the social context (what each viewer knows about each other viewer) must be considered.
Thanks!
This is a really nice and clever anecdote. However, I don’t see why one needs to know game theory to come up with this explanation. One question would be: Can the mathematical study of game theory provide insights or predictions that are more specific than what you described above? For example, can it help an advertiser quantify the benefit from a $4m superbowl commercial as compared to other options? (I’m playing devil’s advocate here.)
Hi Ariel—thanks. It’s true, one does not need game theory to come up with this explanation. Ex post, the explanation is in some sense obvious. But that’s a good thing, in my opinion.
Again, I can only speak for myself. I came at the question of Super Bowl advertising (and TV advertising in general) because I was motivated by a purely theoretical question—whether there are any real-world applications to the concept of “common knowledge” (arbitrarily many levels of metaknowledge). Without game theory, I would never have even thought that the price of ads on the Super Bowl was an interesting question. The larger point of the book “Rational Ritual” is that an important aspect of rituals (like the Super Bowl) is how they create common knowledge. People have been studying rituals and ceremonies ever since the ancient Greeks, and this point, in some sense obvious, could have been made long ago by people who are much smarter than I am. But (as far as I know) it wasn’t. I got to stand on the shoulders of game theory.
This argument is pretty specific for social science standards (!) but I can talk about other stuff. Most game theory papers will not be able to help people quantify the benefits of their actions, so that level of specificity might be tough.
Here’s another (related) example—tell me if it is specific enough [smile]! This is from my 1999 paper “Structure and Strategy in Collective Action” at http://www.chwe.net/michael/socio.pdf.
It is obvious that the network of friendships in a society influences its ability to collectively act, for example rebel against a regime. Almost everyone would agree that a society with few friendship connections has a more difficult time rebelling than a society with a rich network.
To make more specific predictions than this, one must use math and model networks explicitly. Many people have done this. For example, many people think of rebellion as spreading like a disease, and your probability of getting a disease is a function of how many of your friends have the disease. Another approach is to let your action (say your degree of rebellion) be a linear function of the actions of your friends (as in Roger Gould’s 1993 paper). These models are not game-theoretic, i.e. they do not model people’s preferences and how they make choices.
However, in a political rebellion, each person cares deeply about how many other people also participate. You are much more likely to participate if you know others will also. The standard way of modeling this is to give each person a “threshold”—a person will rebel if she knows that the total number of people also rebelling is at least her threshold. A person with a high threshold is more wary, and a person with a low threshold is more militant.
In my 1999 paper, I make a game-theoretic model of a political rebellion in which each person learns the thresholds of her friends in the network. It turns out that one interesting result is that your decision to rebel depends not only on what you know about your friends’ thresholds but also whether your friends know each other.
In some sense, this is obvious. If I have many militant friends but they are scattered about, and don’t know each other, then I might not revolt because I don’t know if they have other militant friends. However, if I have militant friends and I know that they all know each other, I am secure that I will not be alone when I rebel.
This argument has very specific implications about which networks are best for inciting rebellion. If you have a disease-like model, then networks which are very “non-local” and scatter widely are best. In a game-theoretic model, more “ingrown” networks, in which a friend of a friend is likely to be a friend, are advantageous. (This corresponds to the distinction between “weak” and “strong” networks made by Mark Granovetter in 1973.)
This argument could be right or wrong when applied to the real world, but it did not exist before game theory. In previous non-game-theoretic models (which could also be right or wrong), whether a person’s friends are friends with each other has no immediate impact on whether a person rebels.
Anyhow, I’m going on too long! I’m sure that other game theorists can chime in about how their own work is relevant.
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Why we use game theory in Quantitative management?
It’s wonderful that you are getting thoughts from this article as well as from our dialogue made at this time.